|Topic:||Hyperbolic groups, Cannon-Thurston maps, and hydra|
|Affiliation:||Cornell University; Member, School of Mathematics|
|Date:||Monday, November 17|
|Time/Room:||2:00pm - 3:00pm/S-101|
Groups are Gromov-hyperbolic when all geodesic triangles in their Cayley graphs are close to being tripods. Despite being tree-like in this manner, they can harbour extreme wildness in their subgroups. I will describe examples stemming from a re-imagining of Hercules' battle with the hydra, where wildness is found in properties of "Cannon-Thurston maps" between boundaries. Also, I will give examples where this map between boundaries fails to be defined. This is joint work with O. Baker.